Our analysis of the statistical descriptors of these degenerate Debye random media also revealed that OPS-DRM are only phase-inversion symmetric with respect to \(S_2\) , while CP-DRM are only phase-inversion symmetric with respect to the \(S_2(r)\)  and \(F_{ss}(r)\) . For OPS-DRM, this lack of symmetry is to be expected because particle models of two-phase media are generally not phase-inversion symmetric [1]}. Conversely, by the nature of its construction, YT-DRM are likely truly phase-inversion symmetric, satisfying condition (REF ). Furthermore, the additional constraint on the pore-size statistics in CP-DRM destroys such higher-order phase-inversion symmetry. We also determined that the percolation thresholds of these three classes of Debye random media are quite different which indicates that disordered, \(S_2\)  degenerate two-phase random media can exhibit a variety of topologies. Interestingly, we found that the Euler characteristic did not accurately predict the percolation thresholds of CP-DRM and OPS-DRM for reasons indicated in Sec. .
